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 Mar 31 answered Logical reason for the intersection of an infinite family of open sets not being necessarily open Mar 31 comment On the equation $3a^2-4b^3=7^c$ There are solutions beyond the trivial $(\pm1,-1,1)$, for example $(\pm13,5,1)$, as well as families of solutions --- if $(a,b,c)$ is a solution, then clearly $(a\cdot 7^{3m}, b\cdot 7^{2m}, c+6m)$ is also a solution for $m>0$. Mar 25 answered General Introduction to Functional and other Mathematic Notations Mar 24 revised How to show $\sum_{n=-\infty}^\infty J_n J_{n+m} = \delta(m)$? deleted 40 characters in body Mar 24 answered How to show $\sum_{n=-\infty}^\infty J_n J_{n+m} = \delta(m)$? Mar 18 answered How to calculate $E[(\int_0^t{W_sds})^n], n \geq 2$ Mar 17 comment Using Black-Scholes Equation to “buy” stocks Yes, and if you want to take into account the risk of bankruptcy, you can model the company as a barrier option... Mar 17 comment Using Black-Scholes Equation to “buy” stocks Short answer is that Black-Scholes is not likely to help you. You may want to look into models of company fundamentals. B-S is a model for pricing derivative instruments (assuming features of the stock, get value of options). [Note that nothing I say should be construed as giving financial advice. I am not a financial advisor.] Mar 17 answered Using Black-Scholes Equation to “buy” stocks Mar 17 comment [Model Theory] Problem No complaints with that one. Mar 17 comment [Model Theory] Problem Elementary equivalence is not the same thing as isomorphism, so this is not sufficient. (Two structures need not even be the same cardinality to be elementarily equivalent.) It is not clear that the assertion that a monoid is generated by a single element is expressible in a first-order sentence in the language with $0$ and $+$. Mar 17 answered Topology exercises Mar 10 comment What does a hat or star means in math? Absolutely! I guess the point is that there is no "standard" usage across all of mathematics, though there are "local" conventions. (Set theorists will have different conventions than K-theorists...) Mar 10 answered What does a hat or star means in math? Mar 8 comment If a basis of a topology has order no greater than the weight, is it contained in all other bases? I would assume it is the weight of the space, the minimum cardinality of a basis. Mar 3 awarded Critic Mar 2 comment How to compute the series $\sum_{n=0}^\infty q^{n^2}$? The series itself is obviously very quickly converging and using a partial sum gives a good estimate. You can use the identity $\theta(-1/\tau) = (-i\tau)^{1/2}\theta(\tau)$ where $\theta(\tau) = \sum_{n=-\infty}^\infty q^{n^2}$ with $q=e^{\pi i \tau}$ to move $q$ near $1$ to near $0$ to get faster convergence for those more slowly convergent points. Mar 2 answered Is it possible to prove that the metric space is an open set without choice? Feb 14 comment What is an efficient algorithm to compute modular exponentiation of stacked exponents? This is Fermat's little theorem: if $\gcd(b,m)=1$ then $b^{m-1}\equiv 1 \pmod{m}$. Feb 12 awarded Commentator